The British have a horrible history of imperialism, but just to be clear, this was mostly carried out the by US, who also have a horrible history of imperialism.
tl;dr Britain has a long history of causing harm to other countries.
Parent is not making stereotypes about people from the UK or US. They are describing the reputation of those two political entities.
As for specifics, I'd refer the unfamiliar to Wikipedia which itself refers to a very limited subset of about hundred or so books on the topic.
Perhaps you'll find some particular aspect or angle of British or US imperialism particularly enlightening and will want to research further.